Question

The antenna current of an AM transmitter is $8A$ when only the carrier is sent, but it increases to $8·96A$ when the carrier is modulated by a single sine wave. Find the percentage modulation.

• A. $60.1\%$
• B. $71\%$
• C. $80.1\%$
• D. $50.1\%$

Answer 1

The correct option is B

$71\%$

Step1: Given data

Antenna current of an AM transmitter$\left(I_c\right)$=$8A$

And the increased current on modulating $\left(I_t\right)=8·96A$

Step 2: Formula used

We know that the modulation index is computed using the formula,

$m=\sqrt{2\left[{\left(\frac{I_t}{I_C}\right)}^2-1\right]}$

Where $\left(I_t\right)=$ increased current on modulating.

$\left(I_c\right)=$ Antenna current of an AM transmitter

$m=$modulation index

Step 3: Calculating modulation percentage:

Substitute the known values in the formula $m=\sqrt{2\left[{\left(\frac{I_t}{I_c}\right)}^2-1\right]}$,

$$\begin{gathered} m=\sqrt{2\left[{\left(\frac{8·96}{8}\right)}^2-1\right]} \\ m=\sqrt{2\left[\frac{80·2816-64}{64}\right]} \\ m=\sqrt{2\times 0·2544} \\ m=0·713 \\ m\simeq 71\% \end{gathered}$$

So, the approximate percentage modulation is $71\%$.

Hence, option B is the correct answer.